Model Reduction For Dynamic Sensor Steering A Bayesian Approach To Inverse Problems
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Model reduction for dynamic sensor steering: a Bayesian approach to inverse problems
In many settings, distributed sensors provide dynamic measurements over a specified time horizon that can be used to reconstruct information such as parameters, states or initial conditions. This estimation task can be posed formally as an inverse problem: given a model and a set of measurements, estimate the parameters of interest. We consider the specific problem of computing in real-time the prediction of a contamination event, based on measurements obtained by mobile sensors. The spread of the contamination is modeled by the convection diffusion equation. A Bayesian approach to the inverse problem yields an estimate of the probability density function of the initial contaminant concentration, which can then be propagated through the forward model to determine the predicted contaminant field at some future time and its associated uncertainty distribution. Sensor steering is effected by formulating and solving an optimization problem that seeks the sensor locations that minimize the uncertainty in this prediction. An important aspect of this Dynamic Sensor Steering Algorithm is the ability to execute in real-time. We achieve this through reduced-order modeling, which (for our two-dimensional examples) yields models that can be solved two orders of magnitude faster than the original system, but only incur average relative errors of magnitude O(10-3). The methodology is demonstrated on the contaminant transport problem, but is applicable to a broad class of problems where we wish to observe certain phenomena whose location or features are not known a priori.
Handbook of Dynamic Data Driven Applications Systems
This Second Volume in the series Handbook of Dynamic Data Driven Applications Systems (DDDAS) expands the scope of the methods and the application areas presented in the first Volume and aims to provide additional and extended content of the increasing set of science and engineering advances for new capabilities enabled through DDDAS. The methods and examples of breakthroughs presented in the book series capture the DDDAS paradigm and its scientific and technological impact and benefits. The DDDAS paradigm and the ensuing DDDAS-based frameworks for systems’ analysis and design have been shown to engender new and advanced capabilities for understanding, analysis, and management of engineered, natural, and societal systems (“applications systems”), and for the commensurate wide set of scientific and engineering fields and applications, as well as foundational areas. The DDDAS book series aims to be a reference source of many of the important research and development efforts conducted under the rubric of DDDAS, and to also inspire the broader communities of researchers and developers about the potential in their respective areas of interest, of the application and the exploitation of the DDDAS paradigm and the ensuing frameworks, through the examples and case studies presented, either within their own field or other fields of study. As in the first volume, the chapters in this book reflect research work conducted over the years starting in the 1990’s to the present. Here, the theory and application content are considered for: Foundational Methods Materials Systems Structural Systems Energy Systems Environmental Systems: Domain Assessment & Adverse Conditions/Wildfires Surveillance Systems Space Awareness Systems Healthcare Systems Decision Support Systems Cyber Security Systems Design of Computer Systems The readers of this book series will benefit from DDDAS theory advances such as object estimation, information fusion, and sensor management. The increased interest in Artificial Intelligence (AI), Machine Learning and Neural Networks (NN) provides opportunities for DDDAS-based methods to show the key role DDDAS plays in enabling AI capabilities; address challenges that ML-alone does not, and also show how ML in combination with DDDAS-based methods can deliver the advanced capabilities sought; likewise, infusion of DDDAS-like approaches in NN-methods strengthens such methods. Moreover, the “DDDAS-based Digital Twin” or “Dynamic Digital Twin”, goes beyond the traditional DT notion where the model and the physical system are viewed side-by-side in a static way, to a paradigm where the model dynamically interacts with the physical system through its instrumentation, (per the DDDAS feed-back control loop between model and instrumentation).
Bayesian Approach to Inverse Problems
Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data. Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems. The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimation. The first three chapters bring the theoretical notions that make it possible to cast inverse problems within a mathematical framework. The next three chapters address the fundamental inverse problem of deconvolution in a comprehensive manner. Chapters 7 and 8 deal with advanced statistical questions linked to image estimation. In the last five chapters, the main tools introduced in the previous chapters are put into a practical context in important applicative areas, such as astronomy or medical imaging.